Wireless radio channels often exhibit time and frequency dispersion (i.e., delay spread and Doppler spread) due to the presence of signal reflectors or scatterers in the environment, as well as the relative motion of transmitters and receivers. As a result, the channel experiences distortion which can cause transmitted symbols to be incorrectly interpreted at the receiving device. Doppler spreading can cause the delay spread (i.e., multipath) to vary with time.
In addition to multipath channel fading, other sources of signal distortion may also be present in wireless communications. For example, white Gaussian noise is generated by many different sources, such as thermal noise, “black body” radiation from the earth or other warm objects, and from the sun. Accordingly, white Gaussian noise not only has to be taken into account in terrestrial-based wireless communications, it also becomes an important consideration in spacebourne wireless communications. That is, wireless communications in space may not suffer from multipath, terrain blockage, interference, etc., but white Guassian noise may still be problematic. An additive white Gaussian noise (AWGN) channel is one in which the only signal impediment is the linear addition of wideband white Gaussian noise with a constant spectral density.
As such, it is often desired to generate white Gaussian noise for use in testing and evaluating wireless communications systems. The transcendental mathematical functions typically used to generate Gaussian noise are fairly complex, and thus are often implemented with software on microprocessors or digital signal processors (DSPs), for example. Yet, as signal bandwidths increase, it becomes very computationally intensive to generate white Gaussian noise in this way. This is true of wideband waveforms due to the large number of noise samples that are required within a given period of time.
Another approach for generating white Gaussian noise is set forth in “A Hardware Gaussian Noise Generator for Channel Code Evaluation” by Lee et al, 11th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, Apr. 9-11, 2003. This paper notes that hardware simulation of channel codes offers the potential of improving code evaluation speed by orders of magnitude over workstation- or PC-based simulation. A hardware-based Gaussian noise generator is described which is used as a key component in a hardware simulation system for exploring channel code behavior at very low bit error rates (BERs) in the range of 10−9 to 10−10. The generator uses non-uniform piecewise linear approximations in computing trigonometric and logarithmic functions. The parameters of the approximation are chosen to enable rapid computation of coefficients from the inputs, while still retaining high fidelity to the modelled functions. The output of the noise generator is said to model a true Gaussian probability distribution function (PDF) even at very high sigma values.
Despite such advancements in white Gaussian noise generation, other approaches may be desirable which do not require relatively complex trigonometric and logarithmic functions.